Question

Find two consecutive positive integers such that the sum of their squares is 841.

Answer 1

Answer:

x² + x - 420 = 0

Step-by-step explanation:

The sum of the squares of two consecutive positive integers is 841.

Assume that the numbers are (x) and (x + 1) respectively.

As said in question, sum and square of those numbers is 841. i.e.

→ (x)² + (x + 1)² = 841

Used identity: (a + b)² = a² + b² + 2ab

→ x² + x² + 1 + 2x = 841

→ 2x² + 2x = 841 - 1

→ 2x² + 2x = 840

Take 2 as common,

→ 2(x² + x ) = 2(420)

→ x² + x = 420

→ x² + x - 420 = 0

Hence, the algebraic representation of the situation is x² + x - 420 = 0.